Free overfall in rough rectangular channels: a computational approach

This paper presents a theoretical model to determine the end depth of a free overfall in horizontally laid rough rectangular channels. A momentum equation based on the Boussinesq approximation was applied to obtain the equation for the end depth. The effect of streamline curvature at the free surface was utilized to develop the differential equation for the flow profile upstream of the free overfall. As direct solutions for the end depth and flow profile cannot be obtained due to implicit forms of the developed equations, an auto-recursive search scheme was evolved to solve these equations simultaneously. The method for estimation of discharge from the known end depth and Nikuradse equivalent sand roughness is also presented. The present model corresponds closely with the experimental observations.